Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization

Autores
Carrió, María Josefina; Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe
Año de publicación
2023
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this work, error estimates are presented for the case in which the regularized solution isobtained by minimizing doubly-generalized Tikhonov-Phillips functionals. The first result is based mainly on an assumption given by a source condition. It is proved that it is possible to replace this assumption by a variational inequality, obtaining analogous result of the error estimate. Finally, relationships are established between the optimality condition associated with the problem, the source condition and the variational inequality. On the other hand, it is known that, in certain cases, the use of two or more penalizing terms is useful. For this reason, generalizations of the results of error estimates are presented for cases in which the regularized solution is a minimizer of doubly-generalized Tikhonov-Phillips functionals with multiple penalizers.
Fil: Carrió, María Josefina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina
Fil: Mazzieri, Gisela Luciana. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Temperini, Karina Guadalupe. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Matemáticas; Argentina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
INVERSE PROBLEMS
TIKHONOV-PHILLIPS
ERROR ESTIMATE
SOURCE CONDITION
VARIATIONAL INEQUALITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/249373
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/249373
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Error Estimates for Doubly-Generalized Tikhonov-Phillips RegularizationCarrió, María JosefinaMazzieri, Gisela LucianaTemperini, Karina GuadalupeINVERSE PROBLEMSTIKHONOV-PHILLIPSERROR ESTIMATESOURCE CONDITIONVARIATIONAL INEQUALITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this work, error estimates are presented for the case in which the regularized solution isobtained by minimizing doubly-generalized Tikhonov-Phillips functionals. The first result is based mainly on an assumption given by a source condition. It is proved that it is possible to replace this assumption by a variational inequality, obtaining analogous result of the error estimate. Finally, relationships are established between the optimality condition associated with the problem, the source condition and the variational inequality. On the other hand, it is known that, in certain cases, the use of two or more penalizing terms is useful. For this reason, generalizations of the results of error estimates are presented for cases in which the regularized solution is a minimizer of doubly-generalized Tikhonov-Phillips functionals with multiple penalizers.Fil: Carrió, María Josefina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; ArgentinaFil: Mazzieri, Gisela Luciana. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: Temperini, Karina Guadalupe. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Matemáticas; Argentina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaSociedade Brasileira de Matemática Aplicada e Computacional2023-03-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/249373Carrió, María Josefina; Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization; Sociedade Brasileira de Matemática Aplicada e Computacional; Trends in Computational and Applied Mathematics; 24; 1; 14-3-2023; 45-612676-0029CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://tema.sbmac.org.br/tema/article/view/1613info:eu-repo/semantics/altIdentifier/doi/10.5540/tcam.2022.024.01.00045info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-17T11:09:38Zoai:ri.conicet.gov.ar:11336/249373instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-17 11:09:38.344CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
title Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
spellingShingle Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
Carrió, María Josefina
INVERSE PROBLEMS
TIKHONOV-PHILLIPS
ERROR ESTIMATE
SOURCE CONDITION
VARIATIONAL INEQUALITY
title_short Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
title_full Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
title_fullStr Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
title_full_unstemmed Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
title_sort Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization
dc.creator.none.fl_str_mv Carrió, María Josefina
Mazzieri, Gisela Luciana
Temperini, Karina Guadalupe
author Carrió, María Josefina
author_facet Carrió, María Josefina
Mazzieri, Gisela Luciana
Temperini, Karina Guadalupe
author_role author
author2 Mazzieri, Gisela Luciana
Temperini, Karina Guadalupe
author2_role author
author
dc.subject.none.fl_str_mv INVERSE PROBLEMS
TIKHONOV-PHILLIPS
ERROR ESTIMATE
SOURCE CONDITION
VARIATIONAL INEQUALITY
topic INVERSE PROBLEMS
TIKHONOV-PHILLIPS
ERROR ESTIMATE
SOURCE CONDITION
VARIATIONAL INEQUALITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this work, error estimates are presented for the case in which the regularized solution isobtained by minimizing doubly-generalized Tikhonov-Phillips functionals. The first result is based mainly on an assumption given by a source condition. It is proved that it is possible to replace this assumption by a variational inequality, obtaining analogous result of the error estimate. Finally, relationships are established between the optimality condition associated with the problem, the source condition and the variational inequality. On the other hand, it is known that, in certain cases, the use of two or more penalizing terms is useful. For this reason, generalizations of the results of error estimates are presented for cases in which the regularized solution is a minimizer of doubly-generalized Tikhonov-Phillips functionals with multiple penalizers.
Fil: Carrió, María Josefina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina
Fil: Mazzieri, Gisela Luciana. Universidad Nacional del Litoral. Facultad de Bioquimica y Ciencias Biologicas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Fil: Temperini, Karina Guadalupe. Universidad Nacional del Litoral. Facultad de Humanidades y Ciencias. Departamento de Matemáticas; Argentina; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description In this work, error estimates are presented for the case in which the regularized solution isobtained by minimizing doubly-generalized Tikhonov-Phillips functionals. The first result is based mainly on an assumption given by a source condition. It is proved that it is possible to replace this assumption by a variational inequality, obtaining analogous result of the error estimate. Finally, relationships are established between the optimality condition associated with the problem, the source condition and the variational inequality. On the other hand, it is known that, in certain cases, the use of two or more penalizing terms is useful. For this reason, generalizations of the results of error estimates are presented for cases in which the regularized solution is a minimizer of doubly-generalized Tikhonov-Phillips functionals with multiple penalizers.
publishDate 2023
dc.date.none.fl_str_mv 2023-03-14
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/249373
Carrió, María Josefina; Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization; Sociedade Brasileira de Matemática Aplicada e Computacional; Trends in Computational and Applied Mathematics; 24; 1; 14-3-2023; 45-61
2676-0029
CONICET Digital
CONICET
url http://hdl.handle.net/11336/249373
identifier_str_mv Carrió, María Josefina; Mazzieri, Gisela Luciana; Temperini, Karina Guadalupe; Error Estimates for Doubly-Generalized Tikhonov-Phillips Regularization; Sociedade Brasileira de Matemática Aplicada e Computacional; Trends in Computational and Applied Mathematics; 24; 1; 14-3-2023; 45-61
2676-0029
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://tema.sbmac.org.br/tema/article/view/1613
info:eu-repo/semantics/altIdentifier/doi/10.5540/tcam.2022.024.01.00045
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.000565

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